Isomorphisms of $\Spin\left( \frac{1}{2}\right) $ to $\SU(1,1)-\mbox{Boson}$: Universal Enveloping and Kangni-type Transformation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911248952590336 |
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| author | Howard, Francis Atta Kangni, Kinvi |
| author_facet | Howard, Francis Atta Kangni, Kinvi |
| contents | In this study we investigate the nexus between the $\Spin (\frac12)$ and the $\SU(1,1)$-quasi boson Lie structure and reveal related properties as well as some decomposition of spin particles. We show that the $\SU(1,1)$-quasi boson has a left invariant Haar measure and we ascertain its spherical Fourier transformation. We finally show that this spherical Fourier transformation of type delta is a Kangni-type transform when the Planck's constant, $\hbar=1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_02855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphisms of $\Spin\left( \frac{1}{2}\right) $ to $\SU(1,1)-\mbox{Boson}$: Universal Enveloping and Kangni-type Transformation Howard, Francis Atta Kangni, Kinvi Mathematical Physics Primary 43A77, 43A90, \\ 16S30, Secondary 22E46, 17B35, 16T05 In this study we investigate the nexus between the $\Spin (\frac12)$ and the $\SU(1,1)$-quasi boson Lie structure and reveal related properties as well as some decomposition of spin particles. We show that the $\SU(1,1)$-quasi boson has a left invariant Haar measure and we ascertain its spherical Fourier transformation. We finally show that this spherical Fourier transformation of type delta is a Kangni-type transform when the Planck's constant, $\hbar=1$. |
| title | Isomorphisms of $\Spin\left( \frac{1}{2}\right) $ to $\SU(1,1)-\mbox{Boson}$: Universal Enveloping and Kangni-type Transformation |
| topic | Mathematical Physics Primary 43A77, 43A90, \\ 16S30, Secondary 22E46, 17B35, 16T05 |
| url | https://arxiv.org/abs/2511.02855 |